Dielectric Relaxation of Spherical Polyelectrolyte Brushes: Movement of Counterions and Electrical Properties of the Brush Layer

Dielectric behaviors of spherical polyelectrolyte brush (SPB) suspensions under various mass fractions of SPB and the pH of solution were investigated in a frequency range of 40 Hz to 110 MHz. The SPB consists of a polystyrene (PS) core grafted with poly(acrylic acid) (PAA) chains. Two unique relaxations were found at either about 10 kHz or 1-10 MHz, respectively, with the former due to the diffusion of counterions and the latter resulting from the interfacial polarization. Using dielectric parameters of two relaxations, we obtained information about the migration of counterion and the conformation of polyelectrolyte chains. The PAA chains are fully stretched when pH is about 8 under the domination of the equilibrium between the penetration and diffusion of counterions in the brushes. A dielectric model is proposed to describe the high-frequency relaxation, and the permittivity and conductivity of SPB and its volume fraction were also calculated on the basis of the model. The surface conductivity of SPB, the Donnan potential, and the fixed charge density in the brush layer were derived from these paramaters. The distribution of the Donnan potential was also simulated by using Poisson-Boltzmann equations, and the result is in accordance with these obtained on the basis of the dielectric model.